The scalar spectral index is presented by [1]}:
\(\begin{array}{llll}n_{s}-1 & = & \frac{d\ln P_{R}(k)}{d\ln (k)} & \\& = & \frac{M_{p}^{2}}{8\pi (A+V^{\left( \alpha +1\right) })^{\frac{1}{\alpha +1}}\left( 1+\frac{(A+V^{\left( \alpha +1\right) })^{\frac{1}{\alpha +1}}}{2\lambda }\right) }\left( -3\frac{V^{\alpha }V^{\prime 2}}{\left(A+V^{\alpha +1}\right) }\frac{\left( 1+\frac{(A+V^{\left( \alpha +1\right)})^{\frac{1}{\alpha +1}}}{\lambda }\right) }{\left( 1+\frac{(A+V^{\left(\alpha +1\right) })^{\frac{1}{\alpha +1}}}{2\lambda }\right) }+2V^{\prime \prime }\right) . &\end{array}\) 
